Nuclear Fusion Enhancement by Heavy Nuclear Catalysts

TL;DR

This work investigates fusion-rate enhancement in hot plasmas due to heavy nuclear catalysts, focusing on gold ($Z=79$) nuclei that generate dense electronic screening around light reacting nuclei. The authors solve a self-consistent, nonlinear Poisson-Boltzmann problem to obtain the short-range polarization potential $φ_{ind}$, finding a near-origin shift of about $14$ keV that adds to weak screening. They derive a Salpeter-like enhancement factor $F_{sc}$ and show a substantial, ~1.5-fold increase in $p-^{11}$B fusion rates above $T\approx 100$ keV, with similar trends for other light-light reactions and a saturation at high temperature. The results suggest measurable effects in laser-plasma experiments and offer a framework to decouple zero-temperature strong screening from thermal screening, with broader implications for understanding screening in astrophysical and laboratory fusion contexts.

Abstract

We seek to understand the effect of high electron density in the proximity of a heavy nucleus on the fusion reaction rates in a hot plasma phase. We investigate quantitatively the catalytic effect of gold ($Z=79$) ions embedded in an electron plasma created due to plasmonic focusing of high-intensity short laser pulses. Using self-consistent strong plasma screening, we find highly significant changes in the internuclear potential of light elements present nearby. For gold, we see a $14\,$keV change in the internuclear potential near the nuclear surface, independent of the long-distance thermal Debye-Hückel screening. The dense polarization cloud of electrons around the gold catalyst leads to a $\sim 1.5$ enhancement of proton-boron ($^{11}$B) fusion above $T=100\,$keV.

Figures (4)

• Figure 1: Depiction of heavy nuclei catalyzing fusion reactions. Two particles (proton and boron) collide in the presence of a large screening cloud of electrons generated by a stationary heavy nucleus such as Au ($Z=79$).
• Figure 2: We show the ratio of the electromagnetic potential energy to the thermal energy for the vacuum potential of gold nuclei. The portion of the potential with strong screening corrections is shown in purple, and the weak screening region is shown in orange. The Gamow energy Eq. (\ref{['eq:gamow']}) for a proton boron reaction probes the strong screening regime
• Figure 3: The potential $e\phi_{\text{ind}}$ due to the induced screening charge density for Fermi-Dirac self-consistent strong screening Eq. (\ref{['eq:Fermi']}) at various temperatures is shown as solid lines ranging from blue to red. The weak polarization potential is shown as dashed lines ranging from blue to red. Overall screening decreases with temperature $T$, but the difference between weak and strong becomes larger for small $T$. The gray area shows the nuclear interior at a radius of $R_\text{Au} = 5.3\,$fm, where the nuclear potential would take over.
• Figure 4: Reaction rate enhancement $\mathcal{F}_\text{sc}$ [see Eq. (\ref{['eq:ratio']})] for various fusion reactions as a function of temperature in keV: p-$^{11}$B as a black solid line, D-T as a dashed blue line, D-D as a dotted red line, and D-$^3$He as a dashed orange line.